Abstract The recently-emerged SARS-CoV-2 B.1.1.529 variant (Omicron) is spreading rapidly in many countries, with a spike that is highly diverged from the pandemic founder, raising fears that it may evade neutralizing antibody responses. We cloned the Omicron spike from a diagnostic sample which allowed us to rapidly establish an Omicron pseudotyped virus neutralization assay, sharing initial neutralization results only 13 days after the variant was first reported to the WHO, 8 days after receiving the sample. Here we show that Omicron is substantially resistant to neutralization by several monoclonal antibodies that form part of clinical cocktails. Further, we find neutralizing antibody responses in pooled reference sera sampled shortly after infection or vaccination are substantially less potent against Omicron, with neutralizing antibody titers reduced by up to 45 fold compared to those for the pandemic founder. Similarly, in a cohort of convalescent sera prior to vaccination, neutralization of Omicron was low to undetectable. However, in recent samples from two cohorts from Stockholm, Sweden, antibody responses capable of cross-neutralizing Omicron were prevalent. Sera from infected-then-vaccinated healthcare workers exhibited robust cross-neutralization of Omicron, with an average potency reduction of only 5-fold relative to the pandemic founder variant, and some donors showing no loss at all. A similar pattern was observed in randomly sampled recent blood donors, with an average 7-fold loss of potency. Both cohorts showed substantial between-donor heterogeneity in their ability to neutralize Omicron. Together, these data highlight the extensive but incomplete evasion of neutralizing antibody responses by the Omicron variant, and suggest that increasing the magnitude of neutralizing antibody responses by boosting with unmodified vaccines may suffice to raise titers to levels that are protective.